Phase stability and electronic structure of ${\mathrm{ScAl}}_3$ and ${\mathrm{ZrAl}}_3$ and of Sc-stabilized cubic ${\mathrm{ZrAl}}_3$ precipitates

The structural stability and the electronic structure of ${\mathrm{ScAl}}_3$ were studied using an all-electron, total-energy, local-density approach. The calculated results show that ${\mathrm{ScAl}}_3$ in the L$1_2$ structure is energetically favored compared with the D$0_{22}$ structure by about 0.42 eV per formula unit. The calculated lattice constant (4.055 Å) is in fairly good agreement with experiment (4.10 Å). As a comparison, the calculated electronic and cohesive properties for ${\mathrm{ZrAl}}_3$ in its metastable L$1_2$ and D$0_{22}$ phases are also presented. It is argued, on the basis of density-of-states results, that a cubic ${\mathrm{Zr}}_{1\mathrm{-}\mathit{x}}$ ${\mathrm{Sc}}_{\mathit{x}}$ ${\mathrm{Al}}_3$ compound (and also ${\mathrm{Ti}}_{1\mathrm{-}\mathit{x}}$ ${\mathrm{Sc}}_{\mathit{x}}$ ${\mathrm{Al}}_3$) might be a good candidate as a dispersed phase in the aluminum alloys for elevated temperature applications. To test this prediction, we determined the electronic structure and the stability of Sc-stabilized cubic (${\mathrm{Zr}}_{0.5}$ ${\mathrm{Sc}}_{0.5}$)${\mathrm{Al}}_3$ using the same total-energy approach. The calculated total energy for (${\mathrm{Zr}}_{0.5}$ ${\mathrm{Sc}}_{0.5}$)${\mathrm{Al}}_3$, which is about 0.24 eV per unit cell lower than the sum of the total energies of ${\mathrm{ZrAl}}_3$ and ${\mathrm{ScAl}}_3$, clearly indicates that cubic (${\mathrm{Zr}}_{0.5}$ ${\mathrm{Sc}}_{0.5}$)${\mathrm{Al}}_3$ is energetically favored compared with a mixture of its constituents. Finally, an analysis of the results indicates that the stability of the aluminides appears to be understood in the rigid-band sense in terms of the band filling of the bonding states.